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No abstract

We study a subclass of Petri nets, called hybrid timed event graphs with multipliers, or equivalently, hybrid timed weighted marked graphs, composed of continuous and discrete graphs interconnected among themselves. Such graphs can be modeled by using a particular algebra, called dioid, defined on a set of operators and endowed with the pointwise minimum operation as addition and the composition operation as multiplication. A just in time control method of these graphs based on residuation theory is proposed.

This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, þ) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, þ) linear model.

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